The ties between alleged Boston Marathon bomber Dzhokhar Tsarnaev and the state’s public higher education system are coming to light at the worst possible time for the University of Massachusetts.

UMass President Robert L. Caret is pushing Beacon Hill for a $39 million funding increase for the next fiscal year — just as taxpayers are absorbing news about Tsarnaev’s outstanding $20,000 tuition bill and apparently poor academic record at UMass Dartmouth. The accused terrorist also had a circle of protective buddies associated with the same campus, who allegedly destroyed evidence connected to the bombing. Two of the friends — Dias Kadyrbayev and Azamat Tazhayakov — are Kazakh nationals who enrolled at the school with student visas. Bad grades invalidated the visas, but that didn’t keep them out of the country or off the campus.

When you’re making a pitch for more taxpayer money, “obviously you never want anything negative about your institution,” Caret acknowledged. But, he added, “the world is not a perfect place. We wish it didn’t happen. Our students are stunned and appalled and hurt. It’s not fair to condemn the entire institution or all our students for what two or three do.”

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Caret is right about this much: Accusations that one student committed an act of terrorism don’t make UMass Dartmouth a breeding ground for terrorists. But the academic requirements for continued enrollment and the tuition policies of a publicly funded institution of higher learning are legitimate areas of taxpayer inquiry, especially when that institution wants more public money.

Citing privacy laws — and with backing from the US Department of Education — UMass won’t release school records for Tsarnaev and friends to the public. However, the records were provided to law enforcement.

Beyond the specifics of the Tsarnaev controversy, there are broader issues for UMass: How many students with poor to failing academic records are allowed to run up tabs across the system, and for how long before they are kicked out? How much coordination exists between university officials and federal agencies when it comes to oversight of the student visa program?

Caret said UMass officials are revisiting vague-sounding policies regarding academic and financial requirements. He also said UMass Dartmouth “handled everything by the book” when it came to notifying federal officials that low grades had invalidated Tazhayakov’s student visa. Yet, 16 days after that notification, Tazhayakov was still able to pass through an airport security checkpoint. “He should not have been allowed back in the country,” said Caret.

For Caret, the extra scrutiny triggered by Tsarnaev’s connection to UMass complicates an already complicated quest for more funding.

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The additional money Caret is seeking would give the five-campus university system a state budget of $478 million for the next fiscal year. It would also move it closer to a 50/50 funding formula, under which the state takes on half the costs of educational programs. UMass hasn’t achieved that critical funding level since Mitt Romney was governor.

Yet even before the April 15 Marathon attack, the extent of political support for UMass was uncertain. Governor Deval Patrick proposed a nearly $2 billion tax package, with $1 billion allotted for transportation improvements and the rest targeted to education needs. The Legislature came up with its own transportation plan, and is still working out the details. On the education side, Patrick’s plan included enough money to get to the 50/50 formula for public higher education. But UMass officials worry the governor might fight harder for companion funding proposals for early childhood education and K-12 programs that are part of his legacy.

Patrick’s budget for the next fiscal year called for a $39 million increase for UMass and the House went along with it. Now the question is whether the Senate will, too. The extra funding would allow UMass to freeze tuition and fees for next year, Caret said.

Concern about fallout from the bombing is spilling over to other campuses. At UMass Lowell, Chancellor Martin T. Meehan said attracting international students is imperative “if you are going to be a world-class, nationally ranked university.”

Meehan said he believes the positives of an internationally diverse campus outweigh the negatives, but acknowledged “there are risks associated with that, and it’s incumbent on all university presidents to look at their policies. We’re double-checking ours.”

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Putting up with bad students who don’t pay their bills — whether they are US or foreign citizens — is another kind of risk that UMass shouldn’t tolerate, especially as it seeks a greater public subsidy.